It’s official: Jersey City Mayor Jerramiah Healy is gunning for a third term.

Though rumors abound that state Sen. Sandra B. Cunningham and Councilwoman at large Viola Richardson are mulling a run for mayor in next year’s city race, for now the only boldface names to make their intentions known are Healy and Ward E Councilman Steve Fulop.

Asked after last night’s State of the City address to say whether he’s definitely in the race, Healy responded simply, “Yes,” while his aides indicated it was a fait accompli.

“There’s no question,” said city Chief of Staff Rosemary McFadden.

City spokeswoman Jennifer Morrill noted that Healy did not announce until January 2009 his intention to seek election to his current term.

Healy, 61, could face an uphill battle. In November, voters in the special election to fill two at-large vacancies on the council tapped Richardson and Rolando Lavarro instead of Healy’s picks for the seats.

Though turnout in that election was a fraction of what it is during the quadrennial city election, the voters’ message was decidedly anti-Healy, with Healy’s candidates coming in fourth and fifth out of 17 hopefuls.

And the mayor is, for now, at a distinct financial disadvantage. Fulop had a roughly $432,000 war chest as of mid-January, having raised $657,512 so far, while Healy is sitting on only about $50,000, according to campaign documents.

At this point in the 2009 campaign, in which Healy vastly outspent his rivals, the mayor had nearly $1 million at his disposal.

Healy was first elected in November 2004 to fill out the remainder of the late Glenn D. Cunningham’s term, winning roughly 2,000 more votes than his closest rival. The following May, he won his first full term resoundingly, nabbing 75 percent of the vote, and he won his second full term in May 2009.

The list of donors to the mayor’s campaign, indicated in his latest campaign filing from January 2012, is a who’s who of high-ranking city officials. McFadden donated $300, as did Planner Bob Cotter, Police Director Sam Jefferson, Business Administrator Jack Kelly and Health Director Harry Melendez.